Moeen and Finn will undergo scans on Friday to discover the full extent of their injuries but it is not thought that the problems are potentially tour-ending.
All-rounder Moeen has suffered pain in his left side since arriving in Australia and sat out of England’s practice session at Perth’s Richardson Park.
Fast bowler Finn, meanwhile, who was added to England’s Ashes squad after Ben Stokes’ involvement in the series was put in jeopardy, hurt his knee while batting in the nets.
Ashes schedule – the key dates
First Test: November 23-27 (Brisbane)
Second Test: December 2-6 (Adelaide)
Third Test: December 14-18 (Perth)
Fourth Test: December 25-29 (Melbourne)
Fifth Test: January 3-7 (Sydney)
Both players will be absent when England start their three-month tour with a two-day game against a West Australian XI at the WACA on Saturday.
Trevor Bayliss’ side will play two more tour matches after this weekend before the first Test starts at Brisbane on November 23.
England will also be without their vice-captain, Ben Stokes, during the first tour match and is appears unlikely that the all-rounder will play a part in any of this winter’s action.
Asked when Stokes will be back available for selection, head coach Trevor Bayliss said on Wednesday: ‘I haven’t got a clue. It’s totally out of our hands. We have just got on with preparing as best we can. I have [written Stokes off].
‘If he turns up it’s an absolute bonus. And if he did happen to turn up, I’m quite sure he would slip back in very easily.’
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